The turbine rotor of a gas turbine engine is usually surrounded in the radial direction by a housing, which is generally known as a heat shield. The heat shield can comprise a number of heat shield segments, whereby the heat shield forms the outer limit of the hot gas flow along the turbine blades. The heat shield also prevents that hot combustion gases penetrate into the space between the heat shield and radially outer turbine housing filled with cooling air. The heat shield can have many different forms, and its inner profile defines the flow cross section of the hot gas flow in the turbine. The turbine blades of the turbine rotor usually have on their radially outer side a surrounding platform, which, depending on the required flow conditions, is either generally cylindrical or generally conical formed. The platform normally has two sealing ribs extending radially outwards from its radially outer side. Honeycomb structures are arranged on the heat shield respectively opposite to the sealing ribs. These honeycomb structures serve to seal the gap between the sealing ribs and the heat shield. The inner profile of the heat shield in a first section provided with the honeycomb structure runs parallel to the axial direction of the turbine. In a second section upstream of the first flat section the inner profile runs at an angle to the axial direction of the turbine. Because the heat shield is subjected to the high temperatures of the hot gas flow and to the high pressure gradient in the flow direction of the hot gases high stress concentrations can arise in the area of the curved section between the first and the second sections. These stresses can significantly reduce the durability of the heat shield.